Algebra: the Key to Student Success, Or Just Another Hurdle?
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Algebra: The Key to Student Success, Or Just Another Hurdle? Sandra Wilder, University of Akron Abstract: The strong emphasis on algebra has led to nationwide school reforms, and it is an integral part of major high school curricula changes that have taken place in recent years. In this article we try to determine if there is a basis for the underlying belief that algebra equips students with the skills necessary to succeed in college. Based on the existing literature, it follows that college algebra may be an indicator of student success in college, but there is no evidence that this subject contributes to that success. There is no evidence of the context or structure of algebra aiding students in developing or even improving any of their cognitive skills, but only their content knowledge. While it is not impossible that this could be the case in a particular situation if the mathematics curricula were constructed with this in mind, no such studies were found in the literature. Keywords. algebra, educational policy, curriculum 1 Introduction he story of algebra, its significance, and most importantly, students’ attitudes toward this subject may be cleverly summed up in a quote from an episode from an American Tsports drama, Friday Night Lights (2012): Tyra Collette: Just wish I could build a time machine, and go back, and shoot whoever it is that invented algebra, that’s for sure. Landry Clarke: Well, see, that’s kind of a Catch-22, though, because in order to invent that time machine you may need to use algebra. While achievement in mathematics has been recognized as an essential requirement for progress and success in STEM fields, knowledge of algebra has been proposed as a necessary condition for overall success in mathematics. The highly accentuated emphasis on algebra in secondary and higher education has led to nationwide school reforms, and it has been an integral part of major high school curricula changes that have taken place in recent years. The importance of this subject has been inflated to the point of being equated to overall success in college. Simply put, success in algebra has been seen as an indicator of Page 48 Ohio Journal of School Mathematics 67 success in college, and it has been suggested to have strong ties to graduation rates (Parker, 2005). The story algebra instruction does not, however, begin in college, but rather many years earlier, in the early grades. We explore the story of this subject while probing into the belief that everyone should take algebra. This notion carries itself through high school and into higher education. Its underlying assumption pertains to a relationship between success in algebra and students’ overall academic achievement. In this article we try to identify if there is a basis for the underlying belief that algebra equips students with the skills necessary to succeed in college. By looking at the studies focusing on algebra, both in K-12 and higher education, we seek to identify algebra as either a predictor of college success or a teachable and necessary skill. In the latter case, the requirement of algebra, even in college majors that are not STEM-based, would be justified as it would result in students acquiring skills transferable to other disciplines. However, if the subject itself does not provide students with skills (other than algebraic ones) that positively contribute to a student’s overall academic achievement, then algebra is merely a predictor of such success. Further, in this work we examine if the belief that success in algebra equals student academic success in secondary and higher education is based on satisfactory quantitative and qualitative research. Another possibility that is considered is that this belief is entirely or in part based on studies that do not correct for the fact that students who do take and succeed in more challenging courses, including algebra, are often the most motivated and high-achieving students. We explore this issue within the existing literature, identifying a possible rationale for the widely accepted stance of “algebra for everyone.” Furthermore, we study the popular belief that there is a causal relationship between the success in algebra and college graduation rates, and how well supported this belief is by the existing literature. 2 Algebra for Everyone? The need for algebra is not as obvious in daily life as is the need for arithmetic or even statistics. In reality, even experts believe that people can function adequately in every aspect of life without algebra (Usiskin, 1995). However, while certain functions can be performed without the aid of algebra, knowledge of the subject certainly allows individuals to work more efficiency. Algebra is the language of generalization and relationships between quantities that allows a person to answer all the questions of a certain type at one time (Usiskin, 1995), and this is the skill that is seen as being valuable regardless of the area of the study in which it is applied. Mathematics, or more specifically, algebra is a gateway to the study of any STEM discipline that students may wish to embark on while in college. It provides or denies a ready access to technically oriented vocational schools, or simply any technically skilled job. This is mainly the reason for encouraging, and recently requiring (in many states), all students to enroll in algebra in the ninth grade. By doing so, students have an opportunity to complete a high school mathematics sequence ending in calculus (Stein, Kaufman, Sherman, & Hillen, 2011). Although the intentions are noble, just how effective are these changes in curriculum, and what is their impact on an overall student academic success? For example, it has been shown that students who take algebra in high school gain in mathematics achievement, regardless of their prior math knowledge; however low-ability Ohio Journal of School Mathematics 67 Page 49 students do not achieve as much from algebra as their higher-ability counterparts (Gamoran & Hannigan, 2000). In 1997, the Chicago Public Schools (CPS) implemented a policy requiring all students to complete a college preparatory curriculum. This included a requiring all students to start taking algebra in ninth grade, instead of having an option of enrolling in remedial math courses for lower-ability students (Allensworth, Nomi, Montgomery, & Lee, 2009). It appears that this policy was at least in part motivated by the same issues that led to the ACT (2008) reports demonstrating that students who complete more rigorous, college preparatory, high school curricula end up performing significantly better on standardized tests. What these reports do not seem to acknowledge, however, is self-selection bias - namely, that higher-achieving students may be more motivated to embark on college preparatory curricula in high school and also prepare more effectively for standardized tests than lower-achieving students. A longitudinal and thorough investigation of the CPS policy revealed results that might not necessarily align with the belief that algebra in high school was beneficial for everyone. For example, students who were required to take algebra starting in ninth grade (according to the implemented policy) were not more likely to attend college, and they were not more likely to pursue math courses beyond the required algebra ones (Allensworth et al., 2009). Surprisingly, higher achieving students were now less likely to go to college after completing the new, college preparatory curriculum (Mazzeo, 2010). Unfortunately, the researchers in this study did not provide any plausible explanations of these outcomes, especially the ones pertaining to higher achieving students. A lack of students pursuing courses beyond algebra is especially significant considering that the highest mathematics course completed in high school remains a strong predictor of bachelor degree completion (Zelkowski, 2010). If the importance of algebra is in student preparation for college, and if the required course did not seem to result in an increase in the number of students pursuing higher education, one must then question the claim that algebra is essential for all students, particularly for those who intend to pursue non-mathematics careers. If the motivation behind “algebra for all” policies is to “push” students toward STEM disciplines, then requiring completion of algebra, a class that some students may not be academically suited for, may not be the best approach. “If students are earning D’s in their courses, can we really expect the content that they are barely learning to matter?” (Allensworth & Nomi, 2009, p. A-5). Studies that focus on the benefit of enrolling in higher level courses often do not correct for self-selection bias, which may make analysis of their results somewhat questionable. Interpretation of high mathematics achievement rates and even graduation rates of students who voluntarily completed higher level mathematics courses needs to be carefully made because “the students who choose to take high level classes are often the most motivated and high-achieving students in their schools” (Mazzeo, 2010, p.2). Chicago Public Schools’ mandatory college preparatory curriculum provided findings independent of students’ motivation to enroll in higher level courses, because once the policy was implemented, every student was required to enroll in an algebra course (Allensworth & Nomi, 2009). However, once the selection bias was controlled, the expected outcomes of this policy were not achieved. For example, the policy was expected to generate improvement in student learning and college readiness, which did not occur. Quite the opposite, it appeared that mandatory curriculum had some negative outcomes. Mathematics grades for lower- skill students declined, and these students were more likely to fail first-year algebra (Allensworth & Nomi, 2009). While lower-skill students were now more likely to earn Page 50 Ohio Journal of School Mathematics 67 algebra credit, their overall grade point average declined (Mazzeo, 2010).